Specific applications, e.g., in the field of plasma physics, require supplying HF currents of more than 1 MW using coaxial lines, whose diameter may not be made arbitrarily large for mechanical and/or HF technology reasons. Particularly in continuous wave mode, such a large quantity of heat per time unit therefore arises on the inner conductor, primarily because of ohmic losses, and in the region of the insulating material struts, primarily because of dielectric losses, that forced cooling is necessary. According to the related art, a gaseous medium is conducted through the annular space between the inner conductor and the outer conductor for forced cooling. However, the quantity of waste heat which may be dissipated in this way is limited, particularly because the pressure and therefore the flow speed of the gaseous coolant may not be increased arbitrarily for a variety of reasons. Liquid media have also previously been used for cooling superconducting coaxial cables, but extensive and costly secondary devices have been necessary for this purpose.